I've been type 1 for 34 years. The only time I've had a problem is when I was flying BMI from Dublin to Heathrow in 2007:
Security agent - "Do you have anything sharp in your carry-on?"
Me - "Yes - insulin pens."
At that point, I was whisked to the side. Another security agent was called over and he asked if I had a doctor's letter. When I responded that I didn't, I was marched out of security back to the British Midland customer service counter. The security guy asked the manager if it was OK that I was carrying insulin in my carry-on without a doctor's letter. She adamantly said no and that I had to check my insulin. I protested and even gave myself an injection in front of them. Nothing. I then proceeded to pretend to put my insulin pens into another bag and check it. I went through security again. When I was asked if I had anything sharp in my carry-on I said no. Sailed through security with no problem.
Returning home, I went to my doctor to get a letter. I always carry the letter, but I never admit to having anything sharp in my carry-on. I am AC Elite - I travel a lot - I've never been stopped except that one time in Dublin when I owned up. Lesson learned - carry a doctor's letter and don't let them know you have diabetic supplies.
As for keeping insulin cool - it will keep at room temperature for a month or more. No need to keep it cold on a flight. That's a myth.